Technical Field
The present invention relates to a matrix generating system and a method thereof, and in particular to a measurement matrix generating system based on scrambling and a method thereof for generating a measurement matrix with high availability.
Related Art
In recent years, with the popularization and development of compressive sensing, compressive sensing becomes widely applied in many fields, for example, in Internet backbone and biomedical signal monitoring systems.
In general, compressive sensing is to obtain a low dimensional measurement value from a high dimensional sparse signal by using a measurement matrix. Therefore, a system only needs to use a low dimensional signal for transmission, and reconstruct, when needed, a low dimensional sampling as a high dimensional signal by using methods such as norm minimization. The compressive sensing has two characteristics: (1) sampling at a frequency lower than Nyquist Theorem so as to reduce a cost and power consumption of a digital-to-analog converter in a sensor; and (2) achieving compression effects while sampling without additional compression hardware, so as to save a cost and power consumption for hardware compression of a traditional sensor.
Traditionally, a compressive sensing measurement matrix often uses a random matrix. However, in order to simplify the technology, improve efficiency, and reduce a storage cost, replacing the random matrix with a structured matrix is also suggested, thereby decreasing the number of elements to be memorized. For example, in the random matrix, there are M×N elements to be memorized. However, in the structured matrix, for example, a circulant matrix as an example, there are only N elements to be memorized; and using a Toeplitz matrix as an example, there are only (M+N−1) elements to be memorized. In this way, as the number of elements to be memorized decreases, a cost for hardware implementation is also significantly reduced. However, the compressive sensing is based on sparse characteristics of signals, and the signals need to be sparse enough to be restored. If the foregoing structured matrix is used as the measurement matrix, it is possible that original signals cannot be restored. Therefore, availability of the measurement matrix is not good.
In view of the above, the problem that availability of the measurement matrix is not good exists in the prior art for a long time. Therefore, it is necessary to provide an improved technical means to solve this problem.